Computational multiscale modeling of carbon nanotube-reinforced polymers

This chapter provides an overview on multiscale approaches applied to carbon nanotube-reinforced polymers (CNRPs). Multiscale methods can be classified into hierarchical or sequential multiscale methods, semiconcurrent multiscale methods, and concurrent multiscale methods. Hierarchical multiscale methods transfer information only from the fine scale to the coarse scale. Classical approaches are computational homogenization or the Cauchy-Born rule; the latter one is usually based on a periodic structure and hence not applicable for CNRPs. In semiconcurrent multiscale methods, information is transferred also back from the coarse scale to the fine scale during the course of the simulation. They seem computationally more feasible for nonlinear responses, as they account only for states that actually occur in the simulation. Many semiconcurrent multiscale methods, such as the FE² approach are based on representative volume elements. In concurrent multiscale methods, the fine scale is directly embedded into the coarse scale. Many interesting results predicting mechanical, thermal, electrical, or chemical properties of CNRPs have been studied with hierarchical multiscale approaches. Far less work on the more complex semiconcurrent or concurrent multiscale methods for CNRPs in turn can be found in the literature. However, these methods promise to address many unresolved aspects, such as fracture.